Subgroups — #44532370

Order 31347.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	3	yes	maximal
2	C₄₃⋊#6855	C₃	1	9	yes	maximal, complemented
3	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	C₃²	1	9	yes	—
5	C₃²⋊(C₄₃⋊C₉)	—	3	9	no	—
6	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
7	C₃×3₋¹⁺²×C₄₃	—	3	3	no	—
8	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
9	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
10	C₃×C₄₃⋊C₉	—	3	9	no	—
11	C₃×C₄₃⋊C₉	—	3	27	no	—
12	C₃³×C₄₃	—	3	3	no	—
13	C₃³×C₄₃	—	3	9	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
15	C₃³×C₄₃	C₃³	1	1	yes	characteristic
16	3₋¹⁺²×C₄₃	—	3	27	no	—
17	C₃×C₉×C₄₃	—	3	3	no	—
18	C₃×C₉×C₄₃	—	3	6	no	—
19	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	—
20	#10624570	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	3	3	no	—
22	C₃²×C₄₃	—	3	9	no	—
23	C₃²×C₄₃	—	9	9	no	—
24	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
25	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
26	C₃²×C₄₃	#737	1	9	yes	—
27	C₉×C₄₃	—	3	9	no	—
28	C₄₃⋊C₉	—	9	9	no	—
29	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
30	C₃×C₃²⋊C₉	—	43	3	no	—
31	#6855	—	43	9	no	—
32	C₃×C₄₃	—	9	3	no	—
33	C₃×C₄₃	#6891	1	1	yes	characteristic
34	C₃×C₄₃	#6893	1	3	yes	—
35	C₃×C₄₃	#6899	1	9	yes	—
36	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	3	no	—
38	C₃×3₋¹⁺²	—	3	9	no	—
39	C₃²×C₉	—	43	9	no	—
40	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
41	C₃²⋊C₉	—	129	9	no	—
42	C₄₃	#10624570	1	1	yes	characteristic, complemented, Sylow
43	C₃³	—	3	3	no	—
44	C₃³	—	3	9	no	—
45	C₃³	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
46	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
47	3₋¹⁺²	—	3	27	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	—	3	6	no	—
50	C₃×C₉	—	129	9	no	—
51	C₃×C₉	—	129	27	no	—
52	C₃×C₉	#11923958	1	9	yes	—
53	C₃²	—	3	3	no	—
54	C₃²	—	3	9	no	—
55	C₃²	—	9	9	no	—
56	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
57	C₃²	C₃×#11923958	1	3	yes	—
58	C₃²	#16812526	1	9	yes	—
59	C₉	—	3	9	no	—
60	C₉	—	387	9	no	—
61	C₃	—	9	3	no	—
62	C₃	#23782798	1	1	yes	characteristic
63	C₃	#23782809	1	3	yes	—
64	C₃	#23782838	1	9	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃³×C₄₃	C₃³
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624570
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃²×3₋¹⁺²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄₃⋊#6855	C₃	semidirect
42. C₄₃	#10624570	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₄₃⋊#6855	3
C₃²×3₋¹⁺²×C₄₃	3
#10624570	43